Existing machine learning techniques have only limited capabilities of handling computationally intractable domains. This research extends explanation-based learning techniques in order to overcome such limitations. It is based on a strategy of sacrificing theory accuracy in order to gain tractability. Intractable theories are approximated by incorporating simplifying assumptions. Explanations of teacher-provided examples are used to guide a search for accurate approximate theories. The paper begins with an overview of this learning technique. Then a typology of simplifying assumptions is presented along with a technique for representing such assumptions in terms of generic functions. Methods for generating and searching a space of approximate theories are discussed. Empirical results from a testbed domain are presented. Finally, some implications of this research for the field of explanation-based learning are also discussed.